Writing data to file, but not overwriting it.

This is my DataBase class, which has a GUI. On GUI there is a "Add" button and text field. After i have filled text field with name and clicked "Add", it overwrites Users.txt file with text field input. My question is, how can I make so that after I have clicked "Add", it doesn't overwrite existing file, but it adds another name on second line, if there happens to be a name on first line already.